Thanks for the great answer! Exactly what I was looking for.
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dima_bDec 1 '12 at 12:49

Hey, I wrote a short note incorporating your proof, based on this MO question. Would you like to be credited in addition to a usual reference? Plz contact me (see my user page)
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dima_bDec 2 '12 at 16:26

The usual reference http://math.stackexchange.com/a/248559 to this MSE page is enough.
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DidDec 2 '12 at 17:49